Indecomposable explicit abelian group

2013/08/11 by Saharon Shelah, Shelah, Saharon
Computer Science · Mathematics · #03C60 #03C75 #03E55 #03E75 #13C99 #20K20 #20K30 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1308.2394

openalex publication_date 2013/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

(withdrawn.) For every lambda we give an explicit construction of an Abelian group with no non-trivial automorphisms. In particular the group absolutely has no non-trivial automorphisms, hence is absolutely indecomposable. Earlier we knew a stronger existence theorem but only up to a quite large cardinal which was a necessary restriction. In another direction the construction does not use the axiom of choice.

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